Fuzzy Sets and Systems最新文献

The wide usage of large-scale knowledge graphs (KGs) motivates the development of user-friendly interfaces so that knowledge graphs become more readily accessible to a larger population. Natural language-based question answering (QA) systems are widely investigated and developed in the context of KGs, which can provide users with a natural means to retrieve the information they need from KGs without expecting them to know the query language. It is very common that natural language contains linguistic terms (fuzzy terms), and fuzzy (flexible) query has been widely investigated in the context of databases. This paper contributes a QA system with fuzzy terms over KGs called f-KGQA. f-KGQA can deal with different types of questions, including simple questions, complex questions, and questions with fuzzy terms. More importantly, users are provided with a channel to flexibly define their fuzzy terms based on their understanding. Our experimental results demonstrate the effectiveness and applicability of f-KGQA in handling questions with fuzzy terms.

The purpose of the paper is to formulate Choquet integral representation theorems for a monotone functional on a collection of functions in such a way that the representing measures are simultaneously inner and outer continuous on appropriate collections of sets such as open, closed, compact, and measurable. This type of theorem is referred to as the continuous Choquet integral representation theorem and will be discussed in a setting general enough for practical use. The benefits of our results are as follows:

• (i)

  the representing measures are simultaneously inner and outer continuous,

• (ii)

  the collections of sets for which the representing measures are inner and outer continuous are larger than those in previous studies,

• (iii)

  the regularity of the representing measures is also considered, and

• (iv)

  it is possible to handle not only σ-continuous but also τ-continuous functionals.

The main goal of this paper is to introduce new local stability conditions for continuous-time Takagi-Sugeno (T-S) fuzzy systems. These stability conditions are based on linear matrix inequalities (LMIs) in combination with quadratic Lyapunov functions. Moreover, they integrate information on the membership functions at the origin and effectively leverage the linear structure of the underlying nonlinear system in the vicinity of the origin. As a result, the proposed conditions are proved to be less conservative compared to existing methods using fuzzy Lyapunov functions. Moreover, we establish that the proposed methods offer necessary and sufficient conditions for the local exponential stability of T-S fuzzy systems. Discussions on the inherent limitations associated with fuzzy Lyapunov approaches are also given. To illustrate the theoretical results, we provide comprehensive examples that demonstrate the core concepts and validate the efficacy of the proposed conditions.

This paper proposes a protocol-based secure guaranteed cost sampled-data controller design problem of Takagi-Sugeno (T-S) fuzzy system under denial-of-service (DoS) attack and input saturation. First, in the absence of an effective description for the characteristics of received signals on controller, a novel scheduling protocol is proposed according to the characteristics of the round-robin protocol and DoS attack, which can guarantee the specific sequence characteristic for control updates. Then, via introducing input delay approach and switched system modeling method, a time-delay switched system with fixed switching sequence is introduced to describe the considered system with DoS phenomenon. Moreover, some novel control criteria are presented to ensure the resulting closed-loop system reaches a required cost level under the obtained control law. And an optimization problem is proposed to compute the optimal upper of the specified cost level. Finally, a simulation example is presented to demonstrate the effectiveness of the algorithm.

Recently, De Miguel, Bustince and De Baets have conducted a systematic study on convolution lattices based on distributive lattices. There have been few reports on applying non-distributive lattices to a domain of functions. As a complement to their work, in this paper, we carry out an in-depth investigation of convolution operations of the functions between a non-distributive lattice (domain) and a frame (co-domain). We first present an equivalence characterization between non-distributive lattices and idempotent functions and further show that a subset of the set of idempotent functions is closed under convolution operations. We demonstrate that this subset also is a bisemilattice and satisfies the Birkhoff equation under join- and meet-convolution operations. Finally, we analyze and study the lattice structure related to the obtained algebraic structure.

Due to the lack of transitivity of the pseudo-order relation of a proper trellis, its meet and join operations are not increasing. In this paper, we identify weaker forms of increasingness of binary operations that are satisfied by the meet and/or join operation of a trellis or lattice. Some of these forms coincide with the classical notion of increasingness when the trellis is a lattice. Furthermore, we demonstrate the role of these weaker forms in the characterization of the meet and join operations of a trellis, lattice or chain as specific idempotent operations.

This study aims to examine the concept of O-fuzzy ideals of “$L^B$-valued general fuzzy automata” (for simplicity, $L^B$-valued GFA), where $B$ is regarded as a set of propositions about the GFA, and its underlying structure is a complete distributive lattice as a generalization of δ-fuzzy ideals. We provide a necessary and sufficient condition for ${\chi }_{\left\{0\right\}}$ to be an O-fuzzy ideal, and we investigate the relationship between the concepts of O-fuzzy ideals and α-fuzzy ideals in a set $B$. Accordingly, the related notions and the results obtained in this study are clarified and explicated by some examples.

Designing automata minimization algorithms is a significant topic in Automata Theory and Languages with practical applications. In this paper, we develop an efficient minimization algorithm for deterministic fuzzy finite automata over locally finite lattices. More precisely, the algorithm outputs an equivalent minimal crisp-deterministic fuzzy finite automaton for an input fuzzy deterministic finite automaton (FDfA). The running time of the proposed algorithm is polynomial for particular types of locally finite lattices, specifically for max-min-based complete residuated lattices. The intuition behind the proposed algorithm relies on the polynomial minimization algorithm's intuition for ordinary deterministic automata developed by Vazquez de Parga, Garcia, and Lopez (2013) [35]. The motivation for this study comes from the fact that the original algorithm's notions and meanings are lost in the context of fuzzy automata. Thus, we establish a new theoretical foundation that provides the correctness and the polynomial-time nature of this new crisp-minimization algorithm for FDfAs.

The paper contributes to the study of belief merging in many-valued logics, taking both a theoretical and implementation approach motivated by applications in real-world scenarios. We focus, in particular, on the Horn fragment of signed logic. On the one hand, a characterization of the class of models of a signed regular Horn formula and a sufficient condition for a signed Horn merging operator to satisfy logical IC-postulates are provided. On the other hand, an implementation of the belief merging process in the signed regular Horn fragment is presented.

We explore the isomorphism between the idempotent measure monad, which relies on the maximum and addition operations, and the idempotent measure monad, which is built upon the maximum and multiplication operations. One of the implications of this result is the development of a fuzzy integral that utilizes the maximum and addition operations. Additionally, we delve into the study of convexities associated with these monads.